Question
Download Solution PDFIn a 200-m linear race, if A gives B a start of 25 m, then A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 m, the race ends in a dead heat. How long does A take to run 200m?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
In a 200-m linear race, if A gives B a start of 25 m, then A wins the race by 10 seconds.
Formula used
Distance = speed × time
Calculation
Let’s assume speed of A as va and speed of B as vb
Then, in a 200 M race distance run by A = 200 m
Distance run by B after getting head start of 25 M = 175 m
Time taken by A = 200/va
Time taken by B = 175/vb
Since B lacks behind by 10 sec therefore Time taken by B is more as compare to that of A by 10 sec,
⇒ 175/vb - 200/va = 10 ....(1)
if A gives B a start of 45 m, the race ends in a dead heat,
Time taken by B = (200 - 45)/vb = 155/vb
Time taken by A = 200/va
Both finish at same time,
∴ 155/vb = 200/va
⇒ va = 40/31 × vb ----(2)
Putting (2) in (1) we get,
Vb = 2
Time taken by B to complete 200M race would be 175 / 2 = 87.5 seconds
Thus time taken by A would be = 87.5 - 10 = 77.5 second
A takes 77.5 seconds to run 200m.
Alternate Method
In the first case:
A runs = 200m , B runs = (200-25)m = 175m
Let A take x s to run 200m then, B will take (x+10) s for 175m
In the second case:
A runs = 200m, B runs = (200-45)m = 155m
Time taken by B to run 155m = time taken by A to run 200m = x s
From the first and second cases, it is clear that for (175-155)m = 20m extra run B takes 10 s extra time.
Thus speed of B = 20m/10s = 2m/s
Therefore, Time taken by A to run 200m = Time taken by B to run 155m = 155/2 = 77.5 s
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